Calculating the js9 fundamental deviation and its limits
The drawing of a drive shaft calls for a ⌀50 js9 dimension to locate a secondary pulley. The setter asks for the two numerical limits on the tool set-up sheet before cutting the first part of the batch. Without dimensions to the thousandth, there’s no way to set the tool stop or zero the flat-anvil outside micrometer.
Interval values and calculating the js9 deviation
The js9 deviation defines a tolerance that is strictly symmetrical about the zero line: the upper limit is plus half the IT9 tolerance interval, and the lower limit is minus half that same IT9. For a given nominal size, the overall IT9 tolerance depends only on the ISO 286-1 size range the value falls into.
| Nominal range (mm) | IT9 value (µm) | Upper deviation es (mm) | Lower deviation ei (mm) |
|---|---|---|---|
| Over 3 up to 6 | 30 | +0.015 | -0.015 |
| Over 6 up to 10 | 36 | +0.018 | -0.018 |
| Over 10 up to 18 | 43 | +0.0215 | -0.0215 |
| Over 18 up to 30 | 52 | +0.026 | -0.026 |
| Over 30 up to 50 | 62 | +0.031 | -0.031 |
| Over 50 up to 80 | 74 | +0.037 | -0.037 |
| Over 80 up to 120 | 87 | +0.0435 | -0.0435 |
| Over 120 up to 180 | 100 | +0.050 | -0.050 |
For the upper limit, add the positive deviation to the nominal size. For the lower limit, subtract the absolute value of the negative deviation from that same nominal size.
Finding the size range under ISO 286-1
The first step is to place the nominal size in its exact ISO 286-1 size range. Ranges are closed at their upper boundary and open at their lower boundary. A size equal to the upper boundary belongs to the lower range.
Take a nominal size of exactly 50 mm. In the ISO 286-1 table, 50 mm is the upper boundary of the 30 mm to 50 mm range. It doesn’t belong to the 50 mm to 80 mm range. If the size were 50.01 mm, it would move straight into the next range.
The guide on converting ISO 286 fits into numerical limits goes back over the general rules for assigning ranges for other grades such as IT6 or IT7.
Looking up the standard IT9 tolerance grade
Once the size range is confirmed, the table gives the fundamental tolerance IT9. Grade 9 is used mainly in general engineering, for parts assembled without a press fit but needing decent guidance.
In the 30 mm to 50 mm range, the IT9 interval is exactly 62 microns, i.e. 0.062 mm. This value is the total spread allowed between the least and the most material condition of the machined part.
Had the nominal size been 60 mm, the IT9 interval would have risen to 74 microns (0.074 mm), showing how tolerances grow with size.
Splitting the deviations symmetrically about the zero line
Unlike positions H, g or f, the js tolerance position has no offset from the nominal size. The zero line cuts the tolerance interval exactly in half.
The upper deviation is:
es = + IT9 / 2 = + 0.062 / 2 = +0.031 mm
The lower deviation is the same with a negative sign:
ei = - IT9 / 2 = - 0.062 / 2 = -0.031 mm
This perfect symmetry makes CNC programming simpler, because the program origin coincides with the nominal value on the manufacturing drawing.
Final inspection limits
Applying the two deviations to the 50 mm nominal size gives the acceptance limits for the part at the metrology station.
Maximum size allowed:
Max size = 50.000 + 0.031 = 50.031 mm
Minimum size allowed:
Min size = 50.000 - 0.031 = 49.969 mm
The acceptance interval runs from 49.969 mm to 50.031 mm. Any diameter measured outside these values calls for a non-conformity decision during production follow-up.
Full applied example and conformity verdict
A technician inspects a 42CrMo4 steel locating shaft whose dimension on the drawing is ⌀50 js9. The check is done on a surface plate with an outside micrometer calibrated at 20 °C, after leaving the part to stabilise for four hours in the metrology room.
The reading taken in the middle of the guide seat is 50.035 mm.
| Quantity | Value |
|---|---|
| Nominal size read | 50.000 mm |
| ISO 286-1 size range | over 30 and up to 50 mm |
| Matching IT9 interval | 62 µm, i.e. 0.062 mm |
| Symmetrical deviations | +0.031 and -0.031 mm |
| Theoretical limits | 49.969 to 50.031 mm |
| Measured value | 50.035 mm |
Verdict: the measured value exceeds the upper limit by 0.004 mm (4 microns). The part is declared non-conforming for exceeding its upper tolerance. It needs another grinding pass, or a concession if the design office approves the larger assembly clearance.
Common pitfalls when applying the js9 tolerance
The first pitfall concerns rounding the deviations for odd IT9 values. For the 10 mm to 18 mm range, IT9 is 43 microns. Halving it gives 21.5 microns. Rounding to 21 or 22 microns changes the real interval by 1 micron. ISO 286 requires keeping the tenth of a micron (0.0215 mm) on inspection documents.
The second is confusing the lower-case js notation, reserved for shafts (external features), with the capital JS notation, reserved for holes (internal features). Although the deviation is calculated symmetrically in both cases, the inspection report must respect the letter case to keep AS9102 traceability.
The third concerns measuring temperature. A 50 mm steel shaft whose temperature rises by 8 °C in the shop grows by almost 5 microns through thermal expansion. Measuring straight off the CNC lathe leads to rejecting a part that would conform once cooled to 20 °C.
The fourth appears when the limits are typed into the inspection plan by hand. Getting the signs wrong and writing -0.031 / -0.031 cancels the tolerance and blocks production for no reason. To validate dimensions quickly without typing errors, CoteCote’s automatic fit detection modules turn ISO designations into numerical limits instantly, ready for quality inspection.